Date: Mar 18, 2004 11:03 PM
Author: Tim Brauch
Subject: Re: Hex Win Proof?


w.taylor@math.canterbury.ac.nz (Bill Taylor) wrote in
news://716e06f5.0403181938.72a82f90@posting.google.com:

> It is an old theorem that in Hex, once the board has been completely
> filled in with two colours, there *must* be a winning path for one
> or other of them.
>
> Now, I can prove this easily enough mathematically, but I'm wondering
> if there is a simple proof, or proof outline, that would be
> understandable and reasonably convincing to the intelligent layman.
>
> Can anyone help out please?
>


Here's what I'm thinking...

Suppose you have red going top-bottom and blue going left-right. If red
does not win, then there must be a path that divides the board into to
pieces, a top and a bottom piece. Red cannot be in any position in that
path, so it must be blue. Thus blue wins. Rotate pi/2 and switch colors.
QED

- Tim

--
Timothy M. Brauch
Graduate Student
Department of Mathematics
Wake Forest University

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